But \(A^c\)  is an assertion too, so it follows from the “for all \(A\) ” part of (REF ) that the right-hand side is bounded by \(\alpha \) , hence the second event in (REF ) has controllably small probability. Finally, our definition of strong prediction validity differs from the predictive belief function calibration property of, e.g., [1]}, as discussed in [2]}.
